Only six of the nearly seventy known rank-two theories [1]} have a vacuum character satisfying an untwisted order-four MDE; most of them have characters satisfying a twisted order-four MDE. So even the simplest extension of our scan to twisted fourth-order is expected to have a large payoff. This extension is conceptually straightforward, but rather challenging from a computational viewpoint. A solution of a fourth-order twisted MDE is specified by eight parameters, and thus the number of cases that serve as input would be too large for a scan as thorough as the one given here. One might hope to implement a more limited scan (e.g. searching for cases with no or small-dimensional flavor symmetry)
or parallelize on a cluster. More speculatively, since we now have a method for generating large data sets of consistent versus inconsistent inputs (in the form of tuples of integers), one might envision the use of
machine learning techniques.
